Tailoring Dense, Orientation–Tunable, and Interleavedly Structured Carbon‐Based Heat Dissipation Plates

Abstract The controllability of the microstructure of a compressed hierarchical building block is essential for optimizing a variety of performance parameters, such as thermal management. However, owing to the strong orientation effect during compression molding, optimizing the alignment of materials perpendicular to the direction of pressure is challenging. Herein, to illustrate the effect of the ordered microstructure on heat dissipation, thermally conductive carbon‐based materials are fabricated by tailoring dense, orientation–tunable, and interleaved structures. Vertically aligned carbon nanotube arrays (VACNTs) interconnected with graphene films (GF) are prepared as a 3D core‐ordered material to fabricate compressed building blocks of O–VA–GF and S–VA–GF. Leveraging the densified interleaved structure offered by VACNTs, the hierarchical O–VA–GF achieves excellent through‐plane (41.7 W m−1 K−1) and in‐plane (397.9 W m−1 K−1) thermal conductivities, outperforming similar composites of S–VA–GF (through‐plane: 10.3 W m−1 K−1 and in‐plane: 240.9 W m−1 K−1) with horizontally collapsed carbon nanotubes. As heat dissipation plates, these orderly assembled composites yield a 144% and 44% enhancement in the cooling coefficient compared with conventional Si3N4 for cooling high‐power light‐emitting diode chips.


First-principle calculations
We have employed the Vienna Ab Initio Package (VASP) [S1] to perform all the density functional theory (DFT) calculations within the generalized gradient approximation (GGA) using the PBE [S2] formulation. We have chosen the projected augmented wave (PAW) potentials [S3] to describe the ionic cores and take valence electrons into account using a plane wave basis set with a kinetic energy cutoff of 400 eV. Partial occupancies of the Kohn−Sham orbitals were allowed using the Gaussian smearing method and a width of 0.05 eV. The electronic energy was considered self-consistent when the energy change was smaller than 10 −5 eV. A geometry optimization was considered convergent when the force change was smaller than 0.02 eV/Å. Grimme's DFT-D3 methodology [S4] was used to describe the dispersion interactions.
The equilibrium lattice constant of hexagonal graphene unit cell separated by a vacuum layer in the depth of 15 Å was optimized, when using a 15×15×15 Monkhorst-Pack k-point grid for Brillouin zone sampling, to be a=2.468 Å. The equilibrium lattice constant of cubic β-SiO 2 unit cell was optimized, when using a 4×4×4 Monkhorst-Pack k-point grid for Brillouin zone sampling, to be a=7.440 Å. The equilibrium lattice constant of cubic β-SiC unit cell was optimized, when using a 11×11×11 Monkhorst-Pack k-point grid for Brillouin zone sampling, to be a=4.368 Å. atoms were allowed to relax.
The CNT/SiO 2 (001)/graphene heterojunction (VACNTs@ SiO 2 -GF) was built; the CNT part comprises of 48 C atoms. the SiO 2 (001) part has a p (2×3) periodicity in the X and Y directions and one stoichiometric layer in the Z direction; the graphene part has a p (6×5·3 0.5 ) periodicity in the X and Y directions and one monolayer in the Z direction. During structural optimizations, the gamma point in the Brillouin zone was used for k-point sampling, and all The CNT/SiC (100)/graphene heterojunction (VACNTs@SiC-GF) was built; the CNT part comprises of 48 C atoms. the SiC (100) part has a p (4×3) periodicity in the X and Y directions and one stoichiometric layer in the Z direction; the graphene part has a (7×3·3 0.5 ) periodicity in the X and Y directions and one monolayer in the Z direction. During structural optimizations, the gamma point in the Brillouin zone was used for k-point sampling, and all atoms were allowed to relax.
The binding energy (E b ) was calculated using the following equation: [S5] where E A/surf is total energy of VACNTs@SiO 2 -GF and VACNTs@SiC-GF systems, E surf is the energy of SiO 2 -GF or SiC-GF, and E A(g) is the energy of VACNTs. The energy of A molecule in a cubic periodic box with a side length of 20 Å and a 1×1×1 Monkhorst-Pack k-point grid for Brillouin zone sampling, respectively. As shown in Table S2, the calculated binding energy for VACNTs@SiO 2 -GF and VACNTs@SiC-GF systems were given. The corresponding optimized location of VACNTs@SiO 2 -GF and VACNTs@SiC-GF were shown in Figure S5.
In addition, we also calculated the charge density difference ∆ρ of VACNTs@SiO 2 -GF and VACNTs@SiC-GF systems using the following formula: [S6] where ρ A/surf was the charge density distribution of VACNTs@SiO 2 -GF or VACNTs@SiC-GF systems, ρ surf was the charge density distribution of SiO 2 -GF or SiC-GF, and ρ A(g) was the charge density distribution of VANCTs. The corresponding charge density distribution of VACNTs@SiO 2 -GF and VACNTs@SiC-GF were given systems in Figure S6 and S7.         heating were simulated using Comsol 6.0 software. [S7] The corresponding simulation models were shown in Figure S16. In order to simplify the Comsol model, we replaced the GF,

Finite element analysis
To understand the role of the heat dissipation plates (HDPs), we used Comsol 6.0 software to simulate the heat transfer process of the cooling system. [S8b, S 9] The model implementation was shown in Figure S20, in which the power density of the heater (LED chip) was set to 10 W cm -2 and the background temperature of the whole system was set to 25 °C. The detailed parameters of the heater, heat sink, and the the three heat dissipation plates (O-VA -GF-1, S-VA -GF-1, Si 3 N 4 ) were listed in Table S4. Figure S21 presented the simulated cross-sectional temperature distribution of the cooling system.  Si-C Si-O-C